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This paper investigates the dynamics of a fourth-order Newtonian iterative method for finding roots of polynomials of degrees three and four. Unlike traditional fourth-order methods requiring third derivatives, this technique avoids them by using the same derivative order in each of its three steps per iteration. When applied to differentiable functions, the method generates chaotic dynamics, as shown for quartic polynomials. Specifically, we apply this root-finding approach to the bifurcation diagram of the logistic map over an interval. Our findings demonstrate the potential for complex behavior even in simple iterative methods, and highlight the usefulness of this approach for exploring polynomial system dynamics. The paper identifies examples of fourth-degree polynomials, explains bifurcation, and chaos. [ABSTRACT FROM AUTHOR]

Background: Treating wide-neck bifurcated cerebral aneurysms (WNBAs) using various techniques and new devices has shown favorable outcomes. However, endovascular coiling can be technically challenging when the aneurysm neck is incorporated into the parent vessel. Furthermore, although recent research has reported favorable outcomes of Neuroform Atlas stent (NAS)-assisted coiling, broad inclusion criteria have hampered precise evaluations of their effectiveness and safety for treating complex WNBAs. Therefore, this study evaluated whether the use of a single NAS is a safe and effective approach for treating complex WNBAs. Methods: We treated 76 complex WNBAs (unruptured, n = 49; ruptured, n = 27) using single NAS-assisted coil embolization and retrospectively analyzed the clinical and angiographic outcomes. Results: In a cohort of 68 patients (mean age, 58.3 ± 11.6 years; males n = 20, 29.4%; females, n = 48, 70.6%), 76 stents were successfully delivered to the target aneurysms, yielding a technical success rate of 98.6%. Complete occlusion was evident in 59 (77.6%) of 76 aneurysms, with neck remnants found in 16 (21.1%) and partial occlusion in 1 (1.3%). Treatment-related morbidities comprised one branch occlusion and one parenchymal hemorrhage. However, no new neurological symptoms of unruptured aneurysms were evident at discharge. The outcomes of 20 of the 27 ruptured aneurysms were favorable (Glasgow Outcome Scale scores of 4 or 5) at the final follow-up assessment (mean 12.2 [6-29] months), except for one initial subarachnoid hemorrhage. Post- treatment angiography revealed complete occlusion in 89.1%, neck remnants in 7.8%, and incomplete occlusion in 3.1% of the aneurysms. Approximately 88.2% of the patients were assessed at least once by follow-up diagnostic or magnetic resonance angiography (mean, 12.5 ± 4.3 [range, 6-29] months), with five (7.8%) minor and two (3.1%) major recurrences. Conclusion: A single NAS is safe and effective for treating WNBAs incorporated into parent vessels. [ABSTRACT FROM AUTHOR]

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In this article, the dynamic behavior and solitary wave solutions of the Akbota equation were studied based on the analysis method of planar dynamic system. This method can not only analyze the dynamic behavior of a given equation, but also construct its solitary wave solution. Through traveling wave transformation, the Akbota equation can easily be transformed into an ordinary differential equation, and then into a two-dimensional dynamical system. By analyzing the two-dimensional dynamic system and its periodic disturbance system, planar phase portraits, three-dimensional phase portraits, Poincar'e sections, and sensitivity analysis diagrams were drawn. Additionally, Lyapunov exponent portrait of a dynamical system with periodic disturbances was drawn using mathematical software. According to the maximum Lyapunov exponent portrait, it can be deduced whether the system is chaotic or stable. Solitary wave solutions of the Akbota equation are presented. Moreover, a visualization diagram and contour graphs of the solitary wave solutions are presented. [ABSTRACT FROM AUTHOR]

In this study, the underlying traits of the new wave equation in extended (3+1) dimensions, utilized in the field of plasma physics and fluids to comprehend nonlinear wave scenarios in various physical systems, were explored. Furthermore, this investigation enhanced comprehension of the characteristics of nonlinear waves present in seas and oceans. The analytical solutions of models under consideration were retrieved using the sub-equation approach and Sardar sub-equation approach. A diverse range of solitons, including bright, dark, combined dark-bright, and periodic singular solitons, was made available through the proposed methods. These solutions were illustrated through visual depictions utilizing 2D, 3D, and density plots with carefully chosen parameters. Subsequently, an analysis of the dynamical nature of the model was undertaken, encompassing various aspects such as bifurcation, chaos, and sensitivity. Bifurcation analysis was conducted via phase portraits at critical points, revealing the system's transition dynamics. Introducing an external periodic force induced chaotic phenomena in the dynamical system, which were visualized through time plots, twodimensional plots, three-dimensional plots, and the presentation of Lyapunov exponents. Furthermore, the sensitivity analysis of the investigated model was executed utilizing the Runge-Kutta method. The obtained findings indicated the efficacy of the presented approaches for analyzing phase portraits and solitons over a wider range of nonlinear systems. [ABSTRACT FROM AUTHOR]

The microvasculature, which makes up the majority of the cardiovascular system, plays a crucial role in the process of thrombosis, with the pathological formation of blood clots inside blood vessels. Since blood microflow conditions significantly influence platelet activation and thrombosis, accurately mimicking the structure of bifurcating microvascular networks and emulating local physiological blood flow conditions are valuable for understanding blood clot formation. In this work, we present an in vitro model for blood clotting in microvessels, focusing on 3D bifurcations that align with Murray's law, which guides vascular networks by maintaining a constant wall shear rate throughout. Using these models, we demonstrate that microvascular bifurcations act as sites facilitating thrombus formation compared to straight models. Additionally, by culturing endothelial cells on the luminal surfaces of the models, we show the potential of using our in vitro platforms to recapitulate the initial clotting in diseases involving endothelial dysfunction, such as Thrombotic Thrombocytopenic Purpura. [ABSTRACT FROM AUTHOR]

In this paper, a predator–prey model with fear-induced group defense and Monod–Haldane functional response is considered. We establish a connection between fear effect and group defense by incorporating anti-predator sensitivity and emphasizing their impact on the dynamics of the model. Our analysis shows that increasing anti-predator sensitivity lowers the threshold for initiating group defense, leading to faster adoption of prey defense strategies. The preliminary results include positivity, boundedness, and persistence. We find that under certain thresholds, anti-predator sensitivity can sustain species persistence; otherwise, predators may face extinction. Changes in anti-predator sensitivity significantly influence system dynamics, notably affecting the quantity and stability of equilibrium points. We provide a comprehensive analysis of the global properties of both boundary and interior equilibrium points. Additionally, the system undergoes Transcritical, Saddle-node and Hopf bifurcation by considering the anti-predator sensitivity as a bifurcation parameter and Bogdanov–Takens bifurcation with respect to the prey birth rate and the anti-predator sensitivity. Numerical simulations support our theoretical findings. Our study highlights the complex interplay of fear effect, group defense, and anti-predator sensitivity in predator–prey dynamics. These results may provide valuable biological insights into predator–prey interactions. [ABSTRACT FROM AUTHOR]

Our paper presents the chaotic behaviour of atmospheric systems with fractional order by using Bernoulli wavelet collocation technique. This technique has not yet been implemented on this model. The study have analysed the dynamics of three climate components—green house gases, temperature and permafrost thaw. To determine the simplicity and efficiency of the developed technique, numerical results have obtained. The combination of graphs and tables shows the stability and efficacy of the developed strategy. Based on the obtained results, we have draw the conclusion that this method offers superior accuracy and efficiency to other methods such as Adam Bashforth's method, Forward Euler's method and fde 12 solver method. This study have reveals the effectiveness of the numerical technique as well as the effect of the non integer derivative on atmospheric models. All calculations have been done using a mathematical program called Matlab. Environmental science can be better understood through these studies. [ABSTRACT FROM AUTHOR]

This study aims to thoroughly investigate the dynamics of a predator–prey model with a Beddington-De Angelis functional response. We assume that the prey refuge is proportional to both species. We establish the standard properties of boundedness, permanence, and local stability. We show that under certain parameter conditions, transcritical bifurcation and Hopf bifurcation occur. To understand the nature of the limit cycle, we determine the direction of the Hopf bifurcation. We focus on the significant ranges of the predators' prey capturing rate and examine how the level of prey fear and the predator's mutual interference affect the system's stability. Through numerical analysis, we study the behavior of the Lyapunov exponent and observe multiple self-repeating shrimp-shaped patterns that indicate periodic attractors in discrete-time predator–prey system. These structures appear across a broad region associated with chaotic dynamics. Additionally, if the intensity of white noise is kept below a specific threshold, the deterministic control approach is equally effective in environmental fluctuation. Numerical simulations support these findings. [ABSTRACT FROM AUTHOR]

Memristor has been extensively employed to emulate neuron/synapse-inspired behaviors and to characterize the electromagnetic induction generated by ionic flowing. A link between memristive features and neural electrical activities is significantly necessary to be investigated. Thus, we propose a new neuron model with a locally active threshold flux-controlled (LTF) memristor, which depicts the electromagnetic induction. The LTF memristive neuron model can exhibit a regular evolution and transition of various firing patterns dependent upon the negative different conductance of the memristor, through performing the corresponding numerical simulations. It is demonstrated that due to the locally active threshold effect, the obtained model has complex firing behaviors. The memristive neural network is connected via chemical synapses. The memristive neural network under the modulation of excitatory and inhibitory chemical synapses shows different synchronous patterns. The captured results reveal that the locally active threshold effect is crucial for the generation of complex firing modes and the emergence of synchronization behaviors. [ABSTRACT FROM AUTHOR]

The carrying capacity's functional dependence illustrates the reality that any species' activities can enhance or diminish its carrying capacity. Migration is the need of many species to achieve better opportunities for survival. In a tri-trophic system, the middle predator often immigrates to consume its prey and often emigrates to secure themselves from predators. This work deals with formulating and investigating a mathematical model reflecting the aforementioned ecological aspects. We perform a detailed analysis to prove the boundedness of the solutions. Further, we examine the existence and stability of equilibrium points, followed by the bifurcation analysis. We explore various global and local bifurcations like Hopf, saddle-node, transcritical, and homoclinic for the critical parameters β (measuring the impact of prey activities on the carrying capacity) and k 1 (measuring the migration rate of a predator). Higher values of β generate unpredictability, which helps explain the enrichment paradox. The presence of a chaotic attractor and bi-stability of node-node type is demonstrated via numerical simulation. The migratory behavior of middle predators can control chaos in the system. Furthermore, we study the proposed model in the presence of seasonal fluctuations. Persistence of the non-autonomous system, existence, and global stability of periodic solutions are analyzed theoretically. The seasonality in β brings the bi-stability between chaotic and periodic attractors, and seasonality in growth rate of the prey causes bi-stability between 2-periodic and 4-periodic attractors. Moreover, the bi-stability in the autonomous system shifts to the global stability of an equilibrium in the seasonal model due to the seasonality in β . When birth and death rates are seasonal along with β , the extinction of one or more populations is possible. The non-autonomous system also exhibits bursting oscillations when seasonality is present in the death rate. Our findings reveal that the population's intense constructive and destructive actions can allow the basal prey to thrive while eradicating both predators. [ABSTRACT FROM AUTHOR]

Understanding and accounting for the slow–fast effect are crucial for accurately modeling and predicting the dynamics of predator–prey models, emphasizing the importance of considering the relative speeds of interacting populations in ecological research. This paper examines a predator–prey interaction to study its complex dynamics due to its slow–fast effect on predator populations. The occurrence and stability of equilibria are analyzed. The stability of positive fixed point is dependent on the slow–fast effect parameter ϵ$$ \epsilon $$, which must fall within a specific range when the generation gap is larger. The positive fixed point becomes unstable for bigger values of ϵ$$ \epsilon $$ because the growth of predators is faster, resulting in the extinction of all prey. Smaller values of ϵ$$ \epsilon $$ cause the positive fixed point to become unstable since the prey grows more quickly while the predator grows more slowly, ultimately causing the extinction of the predator. Moreover, it is shown that Leslie–Gower model experiences Neimark–Sacker and period‐doubling bifurcations at positive equilibrium point. In order to control bifurcation, hybrid control and feedback control methods are employed. Finally, analytical results are confirmed by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider the instability of a constant equilibrium solution in a general activator–inhibitor (depletion) model with passive diffusion, cross‐diffusion, and nonlocal terms. It is shown that nonlocal terms produce linear stability or instability, and the system may generate spatial patterns under the effect of passive diffusion and cross‐diffusion. Moreover, we analyze the existence of bifurcating solutions to the general model using the bifurcation theory. At last, the theoretical results are applied to the spatial water–biomass system combined with cross‐diffusion and nonlocal grazing and Holling–Tanner predator–prey model with nonlocal prey competition. [ABSTRACT FROM AUTHOR]

This paper deals with a model of chemostat with two cross‐feeding species and involving two inhibitions. The excess of hydrogen inhibits the growth of acetogenic bacteria which, in turn, inhibit the growth of methanogenic hydrogenotrophic bacteria. The model is described by a system of four ordinary differential equations. We established the conditions of existence and stability of equilibria with respect to the operating parameters which are the dilution rate and the input substrate concentrations of the species of the model, then we illustrate the operating and bifurcation diagrams. This technique makes it easy to interpret different regions of operating diagrams. Inhibitions let some regions of stability rise and others vanish. [ABSTRACT FROM AUTHOR]

In this paper, we present a memory-based diffusion predator-prey model that incorporates spatial heterogeneity and is subject to homogeneous Dirichlet boundary conditions. Prey species lack memory or cognitive abilities, exhibiting only random diffusion. In contrast, predators utilize memory-based self-diffusion. For the proposed model, we establish the existence and explicit expression of a spatially non-constant positive steady-state. Furthermore, we demonstrate that memory-based diffusion and the averaged memory period can lead to richer dynamics. Specifically, when the memory-based diffusion coefficient is not dominant, the averaged memory period has no impact on the non-constant steady-state. However, when the memory-based diffusion coefficient takes precedence, the averaged memory period can destabilize the non-constant steady-state, resulting in Hopf bifurcation and the emergence of spatially non-homogeneous periodic solutions. [ABSTRACT FROM AUTHOR]

AbstractCompared with traditional composite materials, variable stiffness composite materials with curvilinear fiber paths have higher design flexibility and the potential to improve structural efficiency. In view of this, the nonlinear flutter characteristics of Variable Angle Tow (VAT) composite laminates with thermal effect in supersonic airflow are investigated in this paper. The proposed panel flutter model is developed based on the von Kármán large deformation plate theory. The thermal stress is approximated according to the quasi-steady thermal stress theory, whilst the aerodynamic pressure is calculated based on the first-order piston theory. The aerothermoelastic equations of motion are first established using Hamilton’s variational principle, and the Rayleigh-Ritz method is then applied to solve the governing equations in the space domain. The time-domain nonlinear equations are solved through the fourth-order Runge-Kutta method. The accuracy and convergence of the proposed method are verified through the comparisons with the results available in the literature. The effects of several parameters such as fiber orientation angle, thermal load, and aerodynamic pressure on the nonlinear flutter responses of VAT laminates are comprehensively discussed. Several dynamic behaviors of VAT laminates, including stable flat, buckled, Limit Cycle Oscillation (LCO), multi-periodic motion, quasi-periodic motion, and chaotic motion, are revealed by using the time history, phase portrait, Poincaré map, and bifurcation diagram. The results presented herein may be beneficial for the design of VAT laminates in supersonic airflow. [ABSTRACT FROM AUTHOR]

The nonlinear energy sink (NES) system mainly dissipates energy through damping elements, and changing the position of the damping element will also change the performance of the NES. In this paper, a grounded damping NES is proposed by grounding the damping element of the traditional cubic stiffness NES. The complex dynamics of this two-degree-of-freedom system are investigated. The slow-varying equations of the system under 1:1 internal resonance are derived by using the complexification-averaging (C×A) method, based on which the influence of the primary structure’s damping on a bifurcation is analyzed. The conditions for the existence of strongly modulated response (SMR) are studied, and the accuracy of the results is verified using the slow invariant manifold (SIM), Poincare mapping, and time-history diagrams. This provides a means of verifying the analytical findings. The vibration suppression effects of the grounded damping NES, as compared to the cubic stiffness NES, are thoroughly studied under both pulse and harmonic excitations. The results indicate that the main structure damping affects the stability of the system and the occurrence of the SMR. Most previous studies of the NESs have overlooked the effect of main structure damping, which may influence the selection of structural parameters. Moreover, under relatively large pulse or harmonic excitations, the vibration suppression effectiveness of the grounded damping NES surpasses that of traditional cubic stiffness NES. This finding has important practical significance for improving the vibration suppression effect and robustness of the NES, and provides a reference for the structural design of the NES. [ABSTRACT FROM AUTHOR]

The security performance of image encryption schemes based on chaotic systems has been greatly improved. Specifically, those chaotic systems with high-dimension or special attractors have shown more benefits for enhancing performance. By introducing the tangent function, a 4-dimensional chaotic system with infinite coexisting attractors is constructed. And the dynamical behaviors are analyzed through phase diagrams, bifurcation diagrams, Lyapunov exponent spectrum and spectral entropy complexity diagram. The results demonstrate that the system exhibits self-replication with respect to the initial value y0 and possesses rich dynamical properties, such as infinite coexisting attractors, sensitivity to initial values and period-doubling bifurcation. These characteristics make it suitable for chaotic cryptography applications. Subsequently, a lossless double color image encryption scheme is designed based on the constructed system. The scheme adopts a diffusion-scrambling-diffusion processing method, and cleverly utilizes the information of the original plaintext image in the scrambling process, which significantly enhances the ability to resist known plaintext attacks or selected plaintext attacks. The experimental results verify that the designed algorithm not only effectively encrypts color and grayscale images, but also allows for encryption images of any size. Moreover, the algorithm implementation process is efficient and ensures high security performance, effectively resisting differential attacks, rotation attacks and cropping attacks. This research exploration on the chaotic characteristics of the nonlinear high-dimensional system and its application in image encryption is expected to provide theoretical guidance in the field of secure communication. [ABSTRACT FROM AUTHOR]

This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of small coexistence type bifurcating from the trivial solution and the branches of segregation type bifurcating from points on the branch of small coexistence type. This paper shows the Morse index of steady-states on the branches and constructs the local unstable manifold around each steady-state of which the dimension is equal to the Morse index. [ABSTRACT FROM AUTHOR]

In this paper, a bogie system with time delay is established. The centre manifold theorem and norm form theory are used to reduce the infinite dimensional delay system to the finite dimensional ordinary differential system, and the bifurcation behaviour of the bogie system is analysed. The MatCont toolkit was used to verify the subcritical bifurcation in the system. In addition, the influence of parameters on the bifurcation diagram of the system and the influence of parameters on the critical speed of the bogie system during the hunting motion are also analysed. [ABSTRACT FROM AUTHOR]

Bursting is a crucial form of firing in neurons, laden with substantial information. Studying it can aid in understanding the neural coding to identify human behavioral characteristics conducted by these neurons. However, the high-dimensionality of many neuron models imposes a difficult challenge in studying the generative mechanisms of bursting. On account of the high complexity and nonlinearity characteristic of these models, it becomes nearly impossible to theoretically study and analyze them. Thus, this paper proposed to address these issues by focusing on the midbrain dopamine neurons, serving as the central neuron model for the investigation of the bursting mechanisms and bifurcation behaviors exhibited by the neuron. In this study, we considered the dimensionality reduction of a high-dimensional neuronal model and analyzed the dynamical properties of the reduced system. To begin, for the original thirteen-dimensional model, using the correlation between variables, we reduced its dimensionality and obtained a simplified three-dimensional system. Then, we discussed the changing characteristics of the number of spikes within a burst by simultaneously varying two parameters. Finally, we studied the co-dimension-2 bifurcation in the reduced system and presented the bifurcation behavior near the Bogdanov-Takens bifurcation. [ABSTRACT FROM AUTHOR]

We investigate novel bifurcation phenomena in the generalized KdV–mKdV-like equation. Unlike previous phase diagram studies, we choose variables related to wave speed as the coordinate axis, which led us to discover some interesting bifurcation phenomena. Our method can also be extended to study some other bifurcation phenomena in equations. [ABSTRACT FROM AUTHOR]

The limited availability of formal jobs in developing nations always heightens the challenge for unemployed individuals in securing regular employment. Temporary employment in the informal sector serves as a source to fulfill their basic needs and enhance their employable skills. In this paper, we introduce a nonlinear mathematical model to study the effect of informal and formal jobs on the dynamics of unemployment. For the model formulation, we categorize the labor force into three classes: unemployed, temporary employed, and regularly employed. A separate dynamical variable is used to represent the available temporary vacancies. It is assumed that temporarily employed individuals may transition into regular employment or self-employment. Furthermore, self-employed individuals contribute to generating temporary vacancies within the informal sector. The long-term behavior of the proposed system is analyzed using the qualitative theory of differential equations. A quantity known as the reproduction number of the system is derived, and it is found that the occurrence of multiple bifurcations for the proposed system is influenced by the value of this threshold quantity. Furthermore, we validate our analytical findings numerically. The findings of this study illustrate that an increase in the shifting rate of individuals from temporary to regular employment is not always effective in increasing the number of regularly employed individuals. Additionally, an increase in the transition of temporarily employed individuals into self-employment, coupled with their involvement in creating more temporary jobs, proves beneficial in reducing unemployment. [ABSTRACT FROM AUTHOR]

In this study, we discuss the global dynamics of the Holling-II amensalism model for a strong Allee effect of harmful species. We discuss the existence and stabilization of the extinction equilibria, exclusion equilibria, coexistence equilibria, and infinite singularities by analyzing the presence and stabilization of the system characteristics in terms of the possibilities and correspondences in the model when the death rate of the injured species is used as a threshold value. Also, we find that the two equilibrium points in the first quadrant are effective in proving that the model does not have globally stabilizing features and obtain two critical conditions and their corresponding global phase diagrams. Finally, we explore the weak Allee effect of the victim species, and using the analysis from numerical simulations, we recapitulate the analysis and dynamics of the model in equilibrium. [ABSTRACT FROM AUTHOR]

Memristor synapses have been widely introduced into neuronal models to investigate the effects of external magnetic fields. However, there is a relative lack of research on the external-induced electric fields in neurons. In this paper, a 4D-memristive Hindmarsh–Rose neuron model is constructed by introducing a memristor and an electric field variable, which can generate complex neural firing. Notably, numerical simulations reveal that the initial conditions of the memristor can induce different firing patterns, exhibiting a unique fractal structure in the basin of attractions. Remarkably, the offset parameters of the internal variables of the neuron can be canceled out so that the offset boosting of the variables can be achieved according to the initial values, giving rise to an uncountably many hidden attractors with homogeneous multistability. This model provides the first example of generating uncountably many attractors in a memristive neuron model without relying on trigonometric functions, significantly advancing our understanding of neuronal dynamics. Finally, a digital circuit is designed and implemented on the RISC-V platform to verify the numerical simulation and theoretical analysis. The findings of this study have a certain implication for the development of advanced neuromorphic computing systems and the understanding of complex neuronal behaviors in the presence of external electric fields. [ABSTRACT FROM AUTHOR]

In this paper, the stability and local bifurcations of a composite laminated circular cylindrical shell with radially pre-stretched membranes are explored by using analytical and numerical methods. On the basis of the four-dimensional averaged equation in the case of 1:1 internal resonance, three types of critical points are studied in detail. They are characterized as (1) one pair of purely imaginary eigenvalues and two negative eigenvalues; (2) a simple zero and one pair of purely imaginary eigenvalues; (3) two pairs of purely imaginary eigenvalues in nonresonant case. With the aid of normal form theory and Maple software, the steady-state solutions and the stability regions of the initial equilibrium solutions are obtained. The explicit expressions for the critical bifurcation curves leading to static bifurcation and Hopf bifurcation are also presented. The presence of Hopf bifurcation indicates that the circular cylindrical shell will flutter. The results contribute to the design of reasonable structure parameters to avoid flutter. Finally, numerical simulations are also presented to demonstrate the good agreement with the analytical predictions. [ABSTRACT FROM AUTHOR]

The detachment cliff is a bifurcative transition to partial detachment recently discovered at the DIII-D tokamak (McLean et al 2015 J. Nucl. Mater. 463 533–6). This work presents a database analysis of target parameters in L-mode and H-mode discharges to search for a detachment cliff at ASDEX Upgrade (AUG). Most of the transitions from attached to partially detached divertor conditions observed in H- and L-mode discharges in AUG show bifurcative-like characteristics that are consistent with the properties of the detachment cliff if the B × ∇ B drift is directed towards the active X-point. In the operational space of power and density, the bifurcative transitions identified during an L-mode discharge occur at injected power and density higher than a threshold value ( P tot > 0.7 MW and n e > 1.6 × 10 19 m−3, respectively). Furthermore, the temperatures at which the transitions start are found to be insensitive to the injected impurity, the injected power and the value of the upstream density. Finally, the study of the evolution of the target parameters, of the intensity of the D α line and of specific manometers and bolometer lines of sights shows that the physical process underlying the detachment cliff and the self-sustained divertor oscillations (Heinrich 2020 Nucl. Fusion 60 076013) might be the same. [ABSTRACT FROM AUTHOR]

Summary: This study provides design criteria of multiphase injection locking for an oscillator loop with multiple rotary pulses that can be utilized for an effective frequency multiplier. Coupled oscillator lattice loops can support phase waves. In the case where N pulses rotate in the loop, the oscillatory signal exhibits N times higher frequency than the rotation frequency of a single rotary pulse. Once an external signal succeeds in injection locking the single‐pulse rotation, the loop operates as an efficient N times frequency multiplier. As in a ring oscillator, the progressive multiphase injection locking is best employed, when the loop supports only a single rotary pulse. Because the phase of the external signal becomes different for each pulse, progressive phase assignment does not work well for multiple rotary pulses; therefore, a more efficient scheme of phase assignment is investigated and validated by bifurcation analyses and measurements. The most effective multiphase injection locking is expected for the phase difference between two neighboring oscillators to be set to −4π/N (4π/N), when N pulses rotate to the cell address increases (decreases) in an oscillator loop. [ABSTRACT FROM AUTHOR]

In this manuscript, an attempt is made to investigate the natural convection process in hybrid nanofluid (Al2O3–Cu/water) contained in an isosceles triangular porous conduit with heated side/congruent walls by considering the performance of various thermal conditions. The bottom side of the enclosure is kept isothermally cooled, whereas uniformly and non-uniformly thermal boundary conditions are applied on congruent/side walls. Thermophysical properties of water and nanoparticles are used to model the problem with the help of continuity, momentum, and energy equations. Appropriate combination of variables is used to make the transport equations dimensionless. The obtained partial differential equations (PDEs) have been solved numerically by using Galerkin-based finite element method (GFEM). Trends of Darcy number Da (10 - 5 ≤ Da ≤ 10 - 3) , Rayleigh number Ra (10 3 ≤ Ra ≤ 10 6) , and solid volume fractions ϕ 1 , ϕ 2 (0.00 ≤ ϕ 1 , ϕ 2 ≤ 0.06) on streamlines, local Nusselt number, and isotherms have been presented in pictorial form. Bifurcation analysis is also described to make the contribution more versatile. Finally, results obtained from present simulation are matched for limited version (i.e., ϕ 1 = ϕ 2 = 0.0 ) in order to ensure the accuracy of the GFEM and modeling procedure of the mathematical model. [ABSTRACT FROM AUTHOR]

Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev's potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments. [ABSTRACT FROM AUTHOR]

Murray's law has been viewed as a fundamental law of physiology. Relating blood flow ( Q ˙ ) to vessel diameter (D) ( Q ˙ ·∝·D3), it dictates minimum lumen area (MLA) targets for coronary bifurcation percutaneous coronary intervention (PCI). The cubic exponent (3.0), however, has long been disputed, with alternative theoretical derivations, arguing this should be closer to 2.33 (7/3). The aim of this meta-analysis was to quantify the optimum flow-diameter exponent in human and mammalian coronary arteries. We conducted a systematic review and meta-analysis of all articles quantifying an optimum flow-diameter exponent for mammalian coronary arteries within the Cochrane library, PubMed Medline, Scopus, and Embase databases on 20 March 2023. A random-effects meta-analysis was used to determine a pooled flow-diameter exponent. Risk of bias was assessed with the National Institutes of Health (NIH) quality assessment tool, funnel plots, and Egger regression. From a total of 4,772 articles, 18 were suitable for meta-analysis. Studies included data from 1,070 unique coronary trees, taken from 372 humans and 112 animals. The pooled flow diameter exponent across both epicardial and transmural arteries was 2.39 (95% confidence interval: 2.24–2.54; I2 = 99%). The pooled exponent of 2.39 showed very close agreement with the theoretical exponent of 2.33 (7/3) reported by Kassab and colleagues. This exponent may provide a more accurate description of coronary morphometric scaling in human and mammalian coronary arteries, as compared with Murray's original law. This has important implications for the assessment, diagnosis, and interventional treatment of coronary artery disease. [ABSTRACT FROM AUTHOR]

We continue studies of the nonlocal erosion equation that is used as a mathematical model of the formation of a spatially inhomogeneous relief on semiconductor surfaces. We show that such a relief can form as a result of local bifurcations in the case where the stability of the spatially homogeneous equilibrium state changes. We consider a periodic boundary-value problem and study its codimension- bifurcations. For solutions describing an inhomogeneous relief, we obtain asymptotic formulas and study their stability. The analysis of the mathematical problem is based on modern methods of the theory of dynamical systems with an infinite-dimensional phase space, in particular, on the method of integral manifolds and on the theory of normal forms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of practically susceptible population, which is a fraction of the biologically susceptible population. Assuming that the fraction depends on the severity of the epidemic and the public's level of precaution (as a response of the public to the epidemic), we propose a general framework model with the response level evolving with the epidemic. We firstly verify the well-posedness and confirm the disease's eventual vanishing for the framework model under the assumption that the basic reproduction number R 0 < 1 . For R 0 > 1 , we study how the behavioural response evolves with epidemics and how such an evolution impacts the disease dynamics. More specifically, when the precaution level is taken to be the instantaneous best response function in literature, we show that the endemic dynamic is convergence to the endemic equilibrium; while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a positive periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing "adopting the best response" with "adapting toward the best response", we also explore the adaptive long-term dynamics. [ABSTRACT FROM AUTHOR]

Granular materials belong to the class of complex materials within which rich properties can emerge on large scales despite a simple physics operating on the microscopic scale. Most notable is the dissipative behaviour of such materials mainly through non-linear frictional interactions between the grains which go out of equilibrium. A whole variety of intriguing features thus emerges in the form of bifurcation modes in either patterning or un-jamming. This complexity of granular materials is mainly due to the geometrical disorder that exists in the granular structure. Diverse configurations of grain collections confer to the assembly the capacity to deform and adapt itself against different loading conditions. Whereas the incidence of frictional properties in the macroscopic plastic behavior has been well described for long, the role of topological reorganizations that occur remains much more elusive. This paper attempts to shed a new light on this issue by developing ideas following the configurational entropy concept within a proper statistical framework. As such, it is shown that contact opening and closing mechanisms can give rise to a so-called configurational dissipation which can explain the irreversible topological evolutions that granular materials undergo in the absence of frictional interactions. [ABSTRACT FROM AUTHOR]

In this article, a spatial epidemic model with media coverage is studied. By both mathematical analysis and numerical simulation, we found that there are some typical dynamics of population density such as the formation of the hole, stripe, spot, coexistence of hole and stripe or spot and stripe. The obtained results exhibit that parameters describing media coverage have a significant influence on the spatial pattern of the disease. More specifically, the sequential change in behaviour of the spatial pattern is observed as the parameter that accounts for media coverage increases. These changes analogous to the effect due to the rise in the basic reproduction number. The results presented in this article thus can be applied to any particular disease with some modification to study the effects of media coverage on disease dynamics. The model is although simple but the idea can be well extended to other complex problems. [ABSTRACT FROM AUTHOR]

This study presents an initial study on the bifurcation analysis of bistable oscillator dynamics for human hair-cell bundle structures. The hair-cell bundles within the human cochlea possess highly nonlinear stiffness while sound transmission. To better understand this bistable oscillator dynamics, this study focused on the bifurcation phenomena using the Floquet theory. To define the bifurcations associated with super- and sub-harmonic resonances, the harmonic balance method (HBM) was first utilized with Hill's method, for determining the dynamics stability conditions. In addition, the Floquet multipliers were mapped to examine their relationship with the bifurcation characteristics. To examine the bifurcation characteristics, only the Floquet multipliers associated with unstable conditions were selected because those associated with stable conditions were decaying terms. Then, the complex values of the Floquet multipliers at specific frequency locations were compared with the bifurcations' characteristics. When numerically calculated bifurcations were compared with the results obtained using the HBM, mapping the Floquet multipliers was sufficient for predicting the bifurcations of a biomimetic system inspired by the hair-cell bundle structure. This study suggests practical techniques for employing the HBM with Hill's method by mapping the Floquet multipliers to investigate complex nonlinearities that occur in bistable-stiffness systems. [ABSTRACT FROM AUTHOR]

A mathematical model has been created and investigated that simulates the relationship between predator and prey with the appearance of an infectious disease in the predator population and additional food reservoirs for the predator. The prey declines its rate of growth due to it is enforced by the predator's rage to seek out a place where it will feel scared and safe. The bounds, existence, and uniqueness of the solution of the suggested model are examined. The local stability of the model at feasible equilibrium points was calculated. The Lyapunov function is utilized to identify the basin of attraction for each equilibrium point. The possibility of bifurcation when the parameters vary is also carefully discussed. Numerical simulations were then used to validate the analytical conclusions and provide insight into how parameter changes impacted the model's dynamics. Different attractors of the system are obtained, such as point, periodic, and nonlinear centers. [ABSTRACT FROM AUTHOR]

We show the existence of unbounded connected components of 2π-periodic positive solutions for the equations with one-dimensional Minkowski-curvature operator − u ′ 1 − u ′ 2 ′ = λ a (x) f (u , u ′ ) , x ∈ R , where λ > 0 is a parameter, a ∈ C (R , R) is a 2π-periodic sign-changing function with ∫ 0 2 π a (x) d x < 0 , f ∈ C (R × R , R) satisfies a generalized regular-oscillation condition. Moreover, for the special case that f does not contain derivative term, we also investigate the global structure of 2π-periodic odd/even sign-changing solutions set under some parity conditions. The proof of our main results are based upon bifurcation techniques. [ABSTRACT FROM AUTHOR]

This paper is concerned with stochastic stability and stochastic bifurcation of the FitzhugNagumo model with multiplicative white noise. We employ largest Lyapunov exponent and singular boundary theory to investigate local and global stochastic stability at the equilibrium point. In the rest, the solution of averaging the Ito diffusion equation and extreme point of steady-state probability density function provide sufficient conditions that the stochastic system undergoes pitchfork and phenomenological bifurcations. These theoretical results of the stochastic neuroscience model are confirmed by some numerical simulations and stochastic trajectories. Finally, we compare this approach with Rulkov approach and explain how pitchfork and phenomenological bifurcations describe spiking limit cycles and stability of neuron’s resting state. [ABSTRACT FROM AUTHOR]

In this work, we propose and study a two species Lotka–Volterra competition model, where the first species experiences the mate-finding Allee effect caused by the second species. First, we study the presence and stability of all conceivable positive equilibria and boundary equilibria of this system. Next, by utilizing the Sotomayor theorem, we demonstrate that, given appropriate parameter circumstances, both a saddle-node bifurcation and a transcritical bifurcation exist. Finally, numerical simulations were carried out to validate our theoretical results further. We found that under certain conditions, the system appears to be bistable when the trait-mediated indirect effect is low. However, when the trait-mediated indirect effect is too high, the bistability of the system disappears, and the first species eventually tends to extinction. [ABSTRACT FROM AUTHOR]

Abstract The use of plastic is very widespread in the world and the spread of plastic waste has also reached the oceans. Observing marine debris is a serious threat to the management system of this pollution. Because it takes years to recycle the current wastes, while their amount increases every day. The importance of mathematical models for plastic waste management is that it provides a framework for understanding the dynamics of this waste in the ocean and helps to identify effective strategies for its management. A mathematical model consisting of three compartments plastic waste, marine debris, and recycle is studied in the form of a system of ordinary differential equations. After describing the formulation of the model, some properties of the model are given. Then the equilibria of the model and the basic reproduction number are obtained by the next generation matrix method. In addition, the global stability of the model are proved at the equilibria. The bifurcations of the model and sensitivity analysis are also used for better understanding of the dynamics of the model. Finally, the numerical simulations of discussed models are given and the model is examined in several aspects. It is proven that the solutions of the system are positive if initial values are positive. It is shown that there are two equilibria $$E^0$$ E 0 and $$E^*$$ E ∗ and if $${{\mathcal {B}}}{{\mathcal {R}}}1$$ B R > 1 , the equilibrium $$E^*$$ E ∗ exists and it is globally stable. Also, at $${{\mathcal {B}}}{{\mathcal {R}}}=1$$ B R = 1 the model exhibits a forward bifurcation. The sensitivity analysis of $${{\mathcal {B}}}{{\mathcal {R}}}$$ B R concludes that the rates of waste to marine, new waste, and the recycle rate have most effect on the amount of marine debris.

In this investigation, the analytical behavior of two prominent nonlinear wave equations, namely the doubly dispersive equation (DDE) and the Ablowitz-Kaup-Newell-Segur equation (AKNSE), have been scrutinized. Bifurcation analysis, sensitivity as well as chaotic phenomena are also performed for the earlier-mentioned dynamical systems. These analyzes have profuse applications in the field of electrical circuits and control systems, phase transitions in materials, climate patterns, chemical reaction networks, forecasting market trends, signal processing, and quantum mechanics. Using an advanced mathematical technique, the exact solutions of the mentioned two-wave equations with singular bell-shaped soliton, bell-shaped soliton, anti-bell-shaped soliton, singular soliton, and singular periodic soliton have been studied. The technique utilized in the study is dependable for solving complex nonlinear problems in various natural science and engineering disciplines employed by many researchers. This study identified ten general solutions and ten particular solutions for the two mentioned equations that are novel and precise wave solutions. The solutions obtained in our study are significant not only for understanding the mentioned field but also may be used in revealing other interesting phenomena, such as the analysis of seismology, the study of compulsive collapse, and the study of the material effects and inner construction of solids.

This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour change. The current model also incorporates a new density-dependent treatment that catches the impact of the disease transmission on the treatment. Firstly, we provide a theoretical study of the nonlinear differential equations model obtained. More precisely, we derive the effective reproduction number and, under suitable conditions, prove the stability of equilibria. Afterwards, we show that the model exhibits the phenomenon of backward-bifurcation whenever the bifurcation parameter and the reproduction number are less than one. We find that the bi-stability and backward-bifurcation are not automatically connected in epidemic models. In fact, when a backward-bifurcation occurs, the disease-free equilibrium may be globally stable. Numerically, we use well-known standard tools to fit the model to the data reported for the 2018–2020 Kivu Ebola outbreak, and perform the sensitivity analysis. To control Ebola epidemics, our findings recommend a combination of a rapid behaviour change and the implementation of a proper treatment strategy with a high level of efficacy. Secondly, we propose and analyze a fractional-order Ebola epidemic model, which is an extension of the first model studied. We use the Caputo operator and construct the Grünwald-Letnikov nonstandard finite difference scheme, and show its advantages.

We are concerned with the principal eigenvalue of \begin{equation*} \begin{cases} -\Delta_p u= \lambda\theta_1\varphi_p(v), &x\in \Omega,\\ -\Delta_p v= \lambda\theta_2\varphi_p(u), &x\in \Omega,\\ u=0=v,\ &x\in\partial\Omega \end{cases} \tag{P} \end{equation*} and the global structure of positive solutions for the system \begin{equation*} \begin{cases} -\Delta_p u= \lambda f(v), &x\in \Omega,\\ -\Delta_p v= \lambda g(u), &x\in \Omega,\\ u=0=v,\ &x\in\partial\Omega, \end{cases} \tag{Q} \end{equation*} where $\varphi_p(s)=|s|^{p-2}s$, $\Delta_p s=\text{div}(|\nabla s|^{p-2}\nabla s)$, $\lambda>0$ is a parameter, $\Omega\subset\mathbb{R}^N$, $N> 2$, is a bounded domain with smooth boundary $\partial\Omega$, $f,g:\mathbb{R}\to(0,\infty)$ are continuous functions with $p$-superlinear growth at infinity. We obtain the principal eigenvalue of $(P)$ by using a nonlinear Krein–Rutman theorem and the unbounded branch of positive solutions for $(Q)$ via bifurcation technology.

The pursuit of solitary wave solutions to complex nonlinear partial differential equations is gaining significance across various disciplines of nonlinear science. This study seeks to uncover the solutions to the perturbed nonlinear Schrödinger equation using a robust and efficient analytical method, namely, the generalized exponential rational function technique. This equation is a fundamental tool used in various fields, including fluid mechanics, nonlinear optics, plasma physics, and optical communication systems, and has numerous practical applications across multiple disciplines. The employed method in this study stands out from existing approaches by being more comprehensive and straightforward. It offers a broader range of symbolic structures, surpassing the capabilities of some previously known methods. By applying this method to the perturbed nonlinear Schrödinger equation, we obtain a variety of exact solutions that significantly expand the existing literature and provide a fresh understanding of the model’s properties. Through numerical simulations, we demonstrate the dynamic characteristics of the system, including bifurcation and chaos analysis, and validate our findings by adjusting parameter settings to match expected behaviors.

Bursting is a crucial form of firing in neurons, laden with substantial information. Studying it can aid in understanding the neural coding to identify human behavioral characteristics conducted by these neurons. However, the high-dimensionality of many neuron models imposes a difficult challenge in studying the generative mechanisms of bursting. On account of the high complexity and nonlinearity characteristic of these models, it becomes nearly impossible to theoretically study and analyze them. Thus, this paper proposed to address these issues by focusing on the midbrain dopamine neurons, serving as the central neuron model for the investigation of the bursting mechanisms and bifurcation behaviors exhibited by the neuron. In this study, we considered the dimensionality reduction of a high-dimensional neuronal model and analyzed the dynamical properties of the reduced system. To begin, for the original thirteen-dimensional model, using the correlation between variables, we reduced its dimensionality and obtained a simplified three-dimensional system. Then, we discussed the changing characteristics of the number of spikes within a burst by simultaneously varying two parameters. Finally, we studied the co-dimension-2 bifurcation in the reduced system and presented the bifurcation behavior near the Bogdanov-Takens bifurcation.

Molecular biological networks are highly nonlinear systems that exhibit limit point singularities. Bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) of a molecular network problem represented by the Pettigrew model were performed. The Matlab program MATCONT (Matlab continuation) was used for the bifurcation analysis and the optimization language PYOMO (python optimization modeling objects) was used for performing the multiobjective nonlinear model predictive control. MATCONT identified the limit points, branch points, and Hopf bifurcation points using appropriate test functions. The multiobjective nonlinear model predictive control was performed by first performing single objective optimal control calculations and then minimizing the distance from the Utopia point, which was the coordinate of minimized values of each objective function. The presence of limit points (albeit in an infeasible region) enabled the MNLMPC calculations to result in the Utopia solution. MNLMPC of the partial models also resulted in Utopia solutions.

Abstract This research paper investigates discrete predator-prey dynamics with two logistic maps. The study extensively examines various aspects of the system’s behavior. Firstly, it thoroughly investigates the existence and stability of fixed points within the system. We explores the emergence of transcritical bifurcations, period-doubling bifurcations, and Neimark-Sacker bifurcations that arise from coexisting positive fixed points. By employing central bifurcation theory and bifurcation theory techniques. Chaotic behavior is analyzed using Marotto’s approach. The OGY feedback control method is implemented to control chaos. Theoretical findings are validated through numerical simulations.

We have combined cooperative hunting, inspired by recent experimental studies on birds and vertebrates, to develop a predator-prey model in which the fear effect simultaneously influences the birth and mortality rates of the prey. This differs significantly from the fear effect described by most scholars. We have made a comprehensive analysis of the dynamics of the model and obtained some new conclusions. The results indicate that both fear and cooperative hunting can be a stable or unstable force in the system. The fear can increase the density of the prey, which is different from the results of all previous scholars, and is a new discovery in our study of the fear effect. Another new finding is that fear has an opposite effect on the densities of two species, which is different from the results of most other scholars in that fear synchronously reduces the densities of both species. Numerical simulations have also revealed that the fear effect extends the time required for the population to reach its survival state and accelerates the process of population extinction.